Hypernuclei in Halo/Cluster Effective Field Theory

The light double $\mathrm{\Lambda }$ hypernuclei, ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^4$H and ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^6$He, are studied as three-body $\mathrm{\Lambda }\mathrm{\Lambda }d$ and $\mathrm{\Lambda }\mathrm{\Lambda }\alpha$ cluster systems in halo/cluster effective field theory at leading order. We find that the $\mathrm{\Lambda }\mathrm{\Lambda }d$ system in spin-0 channel does not exhibit a limit cycle whereas the $\mathrm{\Lambda }\mathrm{\Lambda }d$ system in spin-1 channel and the $\mathrm{\Lambda }\mathrm{\Lambda }\alpha$ system in spin-0 channel do. The limit cycle is associated with the formation of bound states, known as Efimov states, in the unitary limit. For the $\mathrm{\Lambda }\mathrm{\Lambda }d$ system in the spin-0 channel we estimate the scattering length $a_0$ for $S$-wave $\mathrm{\Lambda }$ hyperon-hypertriton scattering as $a_0=16.0\pm 3.0$ fm. We also discuss that studying the cutoff dependences in the $\mathrm{\Lambda }\mathrm{\Lambda }d$ and $\mathrm{\Lambda }\mathrm{\Lambda }\alpha$ systems, the bound state of ${}_{\Lambda\Lambda}^{\
4}$H is not an Efimov state but formed due to a high energy mechanism whereas that of ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^6$He may be regarded as an Efimov state.